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melomori [17]
3 years ago
15

A thief steals an ATM card and must randomly guess the correct seven​-digit pin code from a 4​-key keypad. Repetition of digits

is allowed. What is the probability of a correct guess on the first​ try?
Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
7 0

Answer:

The probability of correct guess on the first​ try is \frac{1}{16384}.

Step-by-step explanation:

Consider the provided information.

The ATM has 4 key pad and required a 7 digit pin, where repetition is allowed.

Thief has 7 slots and 4 choices per slot. Because repetition is allowed.

Thus, the total number of different ways are:

4×4×4×4×4×4×4 = 16384

But only one combination is proper code.

Therefore,

\frac{1}{16384}

Hence, the probability of correct guess on the first​ try is \frac{1}{16384}.

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Shirley is going to have her home painted. Tim"s painting charges $250 plus $14 per hour. Colorful paints charges $22 per hour.
Advocard [28]

It would take greater than 31.25 hours for Tim's price to be better. So in terms of whole hours it would take at least 32 hours of work for Tim's price to be better.

5 0
3 years ago
According to the fundamental theorem of algebra, how many zeros does the polynomial below have?
Oxana [17]
It has 3 zeros, because its a polynomial of degree 3.
6 0
3 years ago
Read 2 more answers
What is the inverse of the function f(x) = 2x + 1?
soldier1979 [14.2K]

Answer: The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2


Solution

f(x)=2x+1

y=f(x)

y=2x+1

Isolating x: Subtracting 1 both sides of the equation:

y-1=2x+1-1

y-1=2x

Multiplying both sides of the equation by 1/2:

(1/2)(y-1)=(1/2)2x

(1/2)y-1/2=x

x=(1/2)y-1/2

Changing "x" by "f^(-1) (x)" and "y" by "x":

f^(-1) (x) = (1/2)x-1/2

8 0
3 years ago
where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤
marusya05 [52]

THIS IS THE COMPLETE QUESTION BELOW

The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.

Answer

$168.27

Step by step Explanation

Given p=90000/400+3x

With the limits of 40 to 50

Then we need the integral in the form below to find the average price

1/(g-d)∫ⁿₐf(x)dx

Where n= 40 and a= 50, then if we substitute p and the limits then we integrate

1/(50-40)∫⁵⁰₄₀(90000/400+3x)

1/10∫⁵⁰₄₀(90000/400+3x)

If we perform some factorization we have

90000/(10)(3)∫3dx/(400+3x)

3000[ln400+3x]₄₀⁵⁰

Then let substitute the upper and lower limits we have

3000[ln400+3(50)]-ln[400+3(40]

30000[ln550-ln520]

3000[6.3099×6.254]

3000[0.056]

=168.27

the average price p on the interval 40 ≤ x ≤ 50 is

=$168.27

8 0
3 years ago
The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km) above sea level, then the pres
seraphim [82]

Answer:

373.8mmHg

Step-by-step explanation:

a =height (in km) above sea level,

the pressure P(a) (in mmHg) is approximated given as

P(a) = 760e–0.13a .

To determine the atmospheric pressure at 5.458 km, then we will input into the equation

P(5.458km) = 760e–0.13a .

= 760e^(-0.13×5.458)

=760e^-(0.70954)

= 760×0.4919

=373.8mmHg

Therefore, the atmospheric pressure at 5.458 km is 373.8mmHg

3 0
3 years ago
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